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On the Road

Four vehicles travelled on a road with constant velocities. The car overtook the scooter at 12 o'clock, then met the bike at 14.00 and the motorcycle at 16.00. The motorcycle met the scooter at 17.00 then it overtook the bike at 18.00. At what time did the bike and the scooter meet?

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There and Back

Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?

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At Holborn underground station there is a very long escalator. Two people are in a hurry and so climb the escalator as it is moving upwards, thus adding their speed to that of the moving steps. ... How many steps are there on the escalator?

Speeding Boats

Stage: 4 Challenge Level: Challenge Level:1

Two boats travel up and down a lake, each at a constant speed. They turn at each end without slowing down. The boats start at opposite ends of the lake.

boats on a lake

If the boats travel at the same speed, whereabouts on the lake will they meet for the first time? What about the second time they meet? Other meetings?

What would happen if one boat travelled twice as fast as the other?

Investigate where the boats will meet for other ratios of speeds.

Once you are confident at working with boats travelling at different speeds, why not try this challenge?

Can you work out the length of the lake and the ratio of the speed of the boats from the following information?

  • The boats leave opposite ends A and B at the same instant
  • They cross for the first time 600 metres from A
  • After each boat has turned at the end of the lake, they cross for the second time 400 metres from B
Investigate the ratio of the speeds and the length of the lake when you change these distances. Can you find and prove a general result?

This problem is also available in French: Bateaux Sur Lac